Abstract : In this paper, we propose a new projection operator for the redundancy framework based on a task function defined as the norm of the usual error. This projection operator allows performing secondary tasks even when the main task is full rank. To ensure the convergence of the system, a switching strategy is then defined to switch from the new projection operator to the classical one before the norm of the total error reaches zero. An adaptive gain is also defined to slow down the convergence of the main task. It allows the secondary tasks to be active for longer. The experimental results obtained show the agreement with the analytical study and demonstrate the effectiveness of the proposed projection operator with respect to the classical one.